Analysis of control models based on dFBA for fed-batch bioreactors solved by interior-point methods

Model-based control of bioprocesses based on dynamic flux balance analysis (dFBA) is an interesting strategy due to the possibility of accounting for wider ranges of cellular behaviour and operation conditions than the one based on unstructured models. This type of control models are bi-level optimization problems, since dFBA comprises of differential equations and a linear programming (LP) model. They can be solved with a nonlinear programming (NLP) solver by replacing the LP model with its first-order optimality conditions (KKT conditions) and discretizing the differential equations. When following this approach, it is important to carefully design the optimization problem considering properties of the selected solver. In this work, we show that we can formulate and solve model-based control models with dFBA for fed-batch bioprocesses by using the KKT conditions of the LP model, relaxing the inequality-multiplier complementarities that arise from these conditions and employing a line search interior point solver. We demonstrate this process on a case study that seeks to the maximize growth of Escherichia coli on glucose and discuss fundamental steps that one should carefully evaluate, such as constraint dependence, handling of complementarities and model initialization.